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Decidability of membership problems for flat rational subsets of GL (2, Q) and singular matrices

Abstract:

This work relates numerical problems on matrices over the rationals to symbolic algorithms on words and finite automata. Using exact algebraic algorithms and symbolic computation, we prove new decidability results for 2 × 2 matrices over Q. Namely, we introduce a notion of flat rational sets: if M is a monoid and N ≤ M is its submonoid, then flat rational sets of M relative to N are finite unions of the form L0g1L1 ··· gtLt where all Lis are rational subsets of N and gi ∈ M. We give quite ...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1145/3373207.3404038

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Institution:
University of Oxford
Division:
MPLS
Department:
Computer Science
Role:
Author
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Name:
European Commission
Grant:
648701
Publisher:
Association for Computing Machinery
Host title:
ISSAC '20: Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation
Pages:
122–129
Publication date:
2020-07-20
Acceptance date:
2020-06-01
Event title:
International Symposium on Symbolic and Algebraic Computation (ISSAC 2020)
Event location:
Kalamata, Greece
Event website:
https://www.issac-conference.org/2020/
Event start date:
2020-07-20
Event end date:
2020-07-23
DOI:
ISBN:
9781450371001
Language:
English
Keywords:
Pubs id:
1116416
Local pid:
pubs:1116416
Deposit date:
2020-07-04

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